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arXiv · 2304.00352

Universal approximation of flows of control systems by recurrent neural networks

Miguel Aguiar·Amritam Das·Karl H. Johansson
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Abstract

We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we prove that an architecture based on discrete-time recurrent neural networks universally approximates flows of continuous-time dynamical systems with inputs. The required assumptions are shown to hold for systems whose dynamics are well-behaved ordinary differential equations and with practically relevant classes of input signals. This enables the use of off-the-shelf solutions for learning such flow functions in continuous-time from sampled trajectory data.

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Miguel Aguiar, Amritam Das, Karl H. Johansson. 2023-04-01. Universal approximation of flows of control systems by recurrent neural networks. https://arxiv.org/abs/2304.00352

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